Wear of bit indicator



Feb. 23, 1954 A. LUBINSKI WEAR OF BIT INDICATOR Filed March 29, 1949 3 Sheets-Sheet 1 l/ I I/ II III! II FIG 4A FIG 4 FIG IB FIG IA INVENTOR.

WEAR OF BIT INDICATOR Filed March 29, 1949 3 sh ets-Sheet 2 FIG.9 FIG 9A JNVENTOR.

Patented Feb. 23,1954

OFFICE WEA-R OF BIT INDICATOR Arthur Lubinski, Tulsa, Okla. Application March 29, 1949:, SerialtNo. 84,215

12 Claims.

1 This invention relates to an improvement, in instrumentation to be usedv in drilling" of oil wells and has particular reference; to an arrangement for producing an. indication of the wearof bit used; in; drilling.

When drillingyi'ni very hard formation a bit may be worn out in less than. one hour. ,In soft formation it may be in good condition after many days of service. Whenthe drilling slows down, the driller does not know whether the bit is worn out, or a. hard formation is encountered. The importance of ascertaining the degree, of wear of the bithasbeen recognized in the past, but no satisfactory solution of the problem has been found because the most essential element, causingthe wear, i. e. thehardnessof the formation drilled. is unknown. while drilling.

,It, is the purpose of. this invention toobviate the inconveniences of the prior art and to.- provide the driller with an. instrument indicating on the surface the degree of wear of the bit.

It is another purpose of this invention to provide; an; instrument, that may be incorporated in a great variety of measuring deyiceszused in drill ing operations.

Other and more specific objects of this invention will be readily apparent from the following detailed description when read in conjunction with the accompanying drawingswhich illustrate a form of the apparatus of this invention.

In the drawings:

Fig. 1A and Fig. 1B show schematically certain factors affecting the operation of the proposed'device at; two succeeding times.

Fig. 2 shows the details of the wearof bit indicating instrument in conjunction with conventional drilling equipment.

3 shows the general schematic arrangementof the computer.

Fig. 45 shows the, detailsof an integrating element.

Eig. 4A shows the symbol used for an integrating element of the type shown on Fig. 4.

:FigatiA shows the symbol used for an adding element of the type shown on Fig. 5B and Fig. 5C.

Fig. 5B and: Fig.5C show twomutually perpendicu'lar cross-sections of the adding element.

Fig. oshows the-details ofa multiplying element.

Fig. GA-shows. the symbol used for a multiplyingelementof the type shown on, Fig. 6..

Fig- 7A shows the symbol used for a timing moton,

Tile-8A.. shows the symbol used. for an electromagnetic. transducer of. the type shown orYFig. 8B and ElgZSC.

Fig. 8B and Fig. 8C

transducer.

Fig. 9 shows thedetails of bevel gears for transmission of motion between two perpendicu.-

larshafts.

Fig. 9A. shows. the symbol used for a perpene dicular transmissionof motion of the type shown. on Fig. 9.

This invention is a result of a discovery that,

the rate ofwearof the bit designated by a symbol B is a function which may be expressed as follows:

where We is the weight on bit, i. e. the force-applied by- WB is the bit to the bottom of the hole. measured in thousands of pounds.

1' is the rate of drilling in feet per hour.

s is the number of revolutions per hour of the rotary table.

T is the drilling time in hours. T is equal to zero,

when the drillingstants: with anew bit.

The function B defined by the Expression 1 .the kind and on the size of the bit.

As an illustration of the values of constants, inthe Formula 2 we may choose a rock'bit W'YR, size 9" manufactured by Hughes Tool Company. We -obtain then =4 1 0" feet. revolution for a dullbitz z B 400x RevKLb. x1090).

Foot

spectively, the positions of the drilling string at an instant Ta and at a suitable" later instant T0+AT. Inboth figures thenumeral H d'esiga hates the bore hole in process of being drilled.

The drill string comprises. a drill pipe section I5 show two mutually per-- pendicular cross sections of. the electromagnetic extending from the top of the bore downwards. A heavy and thick drill pipe I! is fastened to the lower portion of the drill pipe and is provided at its lower end with the drill bit IS.

The drill string is subjected during the drilling process to variable tension and therefore its length varies. Of particular interest to the driller are two portions of the drill stem that are represented by points A and B. The point A is located on the top of the drill stem directly above the earth surface. The motion of the point A is directly observable by the driller and can be indicated by means of a suitable arrangement. The point B is located at the lower extremity of the drill string at the bottom of the bore hole. The distance between A and B designated by D represents the length of the drill stem and because of the elasticity of the drill pipe the length D usually undergoes variations caused by variation of corresponding forces.

To use the Formulae 1 or 2 we have to produce an indication of the rate of progress of the bit, and therefore we are particularly interested in determining the downward motion of the lower extremity of the drill represented by the point B. This point is, however, entirely inaccessible to direct observation, and the problem consists therefore in deriving from the motion of point A (directly observable) and from certain factors controlling the length of the drill string, the desired indication of the downward progress of the point B.

Consider now an instant TQ+AT represented in Fig. 1b. The point A has moved downward to a position A distant from A by the amount ADA,

the point B has moved downward to the position B distant from B by the amount ADE and the new length of the drill string represented by the distance A B has now increased to a value D+AD. From the inspection of Fig. 1a and lb it is seen that the following relation holds true:

AB+ADB=ADA+A'B' (3) D+ADB=ADA+D+AD (4) whence ADB=ADA+AD (5) AD AD AD KT AT fir (6) It is desired to produce an indication of the value ADE/AT representing the rate of progress of the bit and it is seen that this value can be determined by separately producing signals representing values ADA/AT and AD/AT and subsequently adding these signals.

The value ADA/AT represents the downward motion of the upper extremity of the drill stem and is represented by means of a suitable arrangement that shall be explained hereafter.

The signal AD/AT representing the rate of change of the length of the drill pipe can be determined by means of the following considerations:

As stated above, the drilling string consists of a relatively thin pipe section 15 which is provided at the lower extremity by a thick pipe I! designated as drill collars which in turn are fastened at their lower ends to the drill bit [8.

It is apparent to those skilled in the art that the drill string is subjected to internal tensions (or compressions) that are not uniform throughout its length, but decrease with the depth. Thus, for instance, the upper portions of the drill string in the neighborhood of the point A are subjected to a tension substantially equal, to the Weight suspended from the hook H. Let Wa designate this weight. As we progress downward, the tension decreases and at a certain critical depth it becomes equal to zero. This critical depth is located below the drill pipe section somewhere within the drill collars section. The section located immediately below this depth is subjected to a small compression and this compression increases with the depth as we approach the point B at the bottom of the hole. At this depth the compression is equal to the weight on the bit. Let We designate this weight.

It is therefore apparent the longest portion of the drill string consists of the drill pipe [5 and is subjected only to tension which causes its elastic elongation. The relatively short section of the drill collars is subjected to compression, but the corresponding elastic deformation is negligible because the thick drill collars are practically nonelastic.

We can therefore consider the overall picture by assuming that the total drill string is subjected to an elastic elongation, and consequently the corresponding variation AD in the length of the drill string can be represented as AD:KAWR where K is a constant (7) AD AW ir iir (8) Consequently, the signal representing the rate of change in the length of the drill stem can be replaced by the signal representing the rate in change in the force We multiplied by an appropriate coefficient.

Substituting 8 in 6 we obtain for the desired representing the progress of the upper extremity of the drill string and the indication i215 dT representing the rate of change of the weight. We may modify somewhat the problem and express the Formula 9 as follows:

dDB d Consequently, as expressed by the Formula 10 the desired result may be obtained by separately producing a signal representing the value DA corresponding to the downward displacement of the upper extremity of the drill string, and separately producing another signal, WR representing the weight suspended on the hook 14. These two signals are subsequently added to form a signal (DA-i-KWR) and subsequently another signal is produced that represents the time derivative of the sum (DA-l-KWR). This latter gives the desired indication representing the rate of drilling, 1. e. the value r in the Formulae 1 and 2.

Wm designates. the total v rweiglrit of thedrillin string... We designates the weightsuspended from the hook I4, i. e. the weight read, on. the weight indicator, and We designates the weight on. bit, or ratherthe upward reaction of the bottom of the hole against thedrilli-ng. string.

Becauseof the vertical equilibrium of the drilling string; following relationholds true:

Consider now Fig. 2 representing a conventional rotary drilling, rig. The'principal portion of the arrangement shown consists of a derrick I mountedon a floor 2', crown: block pulleys 3 from which a conventional traveling block-4 is'suspended by means of the usual. wire cables 5 terminating in the. hoisting or=drilling line "6. The drilling line is fed from the reel I by releasing a conventional brake, not-shown. The movement of the hoisting or drilling line 6- about the crown pulleys-3- controls the raising and lowering-oi traveling block 4. The hoist line 6 afterhavingpassed about the crown block pulleys 3 and the traveling block 'pulley'41 terminates by the socalled dead line B which is. anchored to the derrick. Mounted? on the derrick floor is aconventional rotary table 9"through'which the usual" drilling. string indicated at I0 extendsyinto' the wellfibore II. Drilling string I 0 consists of a-'ro tary' drive member or kelly I2 attached by a swivel-I3 to a'hook' I4 suspended from traveling blockd; hollow" drill pipe I5 connected bya coupling I6 to the Kelly, a hollow thick drillcollar section I! and a, drillibit I8 attached to the lower end-- of the drill collars. An, engine" drivesthe rotary table- 9 through a chain, the-sprocket I09 andthe bevel gears I04. The engine and chain are not shown on the figure.

The; wear of bit indicating instrument comprises the following essential elements:

' ('1) Means comprised within; dotted line I'9 for producing a signal DA. An electricvoltagerepresen-ting thevalue DA is thus produced-across the outputterminals 2'0 and 2] (2-) Means comprised within the dotted line IIl-I-"for producing a signal proportional-"to We, electric A. C. voltage proportional: to We is thusflprod'uced across the output terminals II-I (39 Means comprised within the "dotted rectangle I02 for producinga signalKWR. An electricDa 'C. voltage is thus produced across the output terminals 23 and- 24.

(4") Means for addingthe signals DA andKWn comprised within the dotted rectangle 25'. This means is provided with two' pairs-of input termi'nals designated by numerals 26, 2'1 and 28,129 and one pair of output terminals 30, 31-. Theinput terminals are connected in a manner so as to produce across the output terminals S'Uand 31-2)} voltage equal to-the sum ofthe two input'volt ages. Since the input" voltages applied acros's the terminals 26, '21-" and 2-8 2 9* are respectively" and KWR, then. the. resulting voltage acrossxthe. output terminals 30, 31? represent Didi-PKWR- (5'-) -'*Means'= comprised within thedotted: rec-. tangle 32 for producing the time derivative. oiithe signal 'Dh-PKWR. The means is provided Withl one -pair of input terminals 30, 3| across which a voltagerepresenting the signal Dari-Ewe iszap. pliedand one pair' of outputterminals. 332mm 34* across-which a voltage representing the signal produc d- (6 Means comprised within the dotted rectanglelflfiiior damping the fluctuations due to vibrations and other reasons which frequencies are ofthe same order of magnitude. The means" is provided with one pair of input terminals 3-3;

3'41 one pair of output terminaIs'BB BT. The

voltage across the output terminals 66 and? representsthe rate of progress 1' with which the bitipenetrat'es the formation.

(17); Means comprised within the dotted rec tangle I03"for producing a D. C. si'gna'lWR.

electric C. voltagfi representing. the value of WR is thus produced across the output terminals 23Aand 24A,

(8') Means comprised within the dotted-rectangle IIfIlfor producing a signal s, i. e. a signal of the rotary angular velocity. An electric voltage representing the value of s is thus produced across the output terminals I06 and I01.

(9) A computer IllB'for computing and indieating the values of thefunction B according to the Formula 12. The computer is provided with three pairs of input electric terminals I"I'4II 5, II6-II.'I, and II8-II9. 'The three inputvoltages representv respectively:

Across I I-.4 -II5': r, or rate of drilling.

Across; I. I'Ii-II'I: W or'weight.

Across; I'I;8--I I9: s; or rotary angular velocity; The computer I08 is also-provided withga shaft" 2'19- which drives the hand 222 in frontof thedial' 2'23 and. which indicates the weight on bit W's. Another shaft designated by the numeral 2201's set on an angular position corresponding to the totalweight of the drilling string WT- The set- .ting has to be made immediately before starting drilling with a new section of drilling. pipe I 5 added to the drilling string. As indicatedabove the total weight WT of the drilling string, and consequently the setting of the shaft 220, can: be determined when the bit is ofi'bottom, and consequently thetotal' weight of the drilling string is suspended on the hook Ig4. Under such condition, WB 'O and the value WT is indicated on the dial 223-. with an output shaft cs2, the angular position of which is proportional to B. The hand 294mm front of the. dial 205 indicates the values of B.

(Zlcnsider now more in detail the various means comprised into the wear of bit indicatingarran-gement in accordance with my invention.

(1) The means for producing the signaljD'A (within the dotted line it!) comprises a pulley 3t driven by the hoist line it which in turn drives. aworm gearing reduction 3'! which moves the moving arm 33 of a potentiometer. The potentiometer comprises a semi circular fixed resistor 3fi having its. terminals 48 and 61!? supplied by-a, suitab'l e'batt'ery 42. The arm 38 is providbldiat its. extremity with a to slideupon the resistor the-motion of the gear;

ccor ance contact: member. adapted.

The output" terminaIs 2| and 20 are respectively connected to the ter-' minal 40 of the resistor and the moving arm 38. It is apparent that the output voltage across the terminals 2| and 26 represents in fact the potential drop in a portion of the resistor between the terminal 40 and the sliding contact of the moving arm 38 and, furthermore, this voltage is proportional to the total displacement of the hoist line which in turn is proportional to DA.

(2) The means for producin a signal proportional to We and comprised within the dotted line has as its essential element a strain responsive element 42. This element consists of a resistor having its two'ends fastened by means of appropriately insulated terminals to a frame structure 55 which is in turn clamped to the dead line 8. The dead line is subjected to a tension which is proportional to We. This tension is transmitted to the frame structure 43 and to the strain responsive element 22 and causes a corresponding elongation of this element which in turn causes a corresponding change in the electric resistance of the element. Consequently, the resistance of the element 122 represents the tension We. The strain responsive element 42 is made to be one of the arms of a Wheatstone bridge, the remaining three arms of which consist of resistors 14, 45, and 4-5. The two terminals 41 and 48 of the bridge are supplied with an A.C. voltage source 49. Consequently, the output voltage across the two bridge terminals 56 and represents We. The same signal amplified in the amplifier 52 appears across the output terminals ill and H2.

(3) The means for producing a signal representing KWR. (within the dotted rectangle I02) comprises a manually set autotransformer 53, a transformer 54, a tw0-wave rectifier 55, and a resistor 56. The autotransiormer 53 may be of any commercial type such as the Varitran manufactured by General Electric. It produces a means of changing at will the ratio between the tension We and the output voltage across the terminals 23 and 24, said output voltage representing the Value KWR. Thus a suitable value may be given to the coefficient K (see Formula in accordance with the elasticity of the pipe. It is well known that the elasticity of the drill pipe depends upon the type of the pipe and its length. Consequently the values of K have to be changed from time to time as the drilling progresses.

(4) The means for producing the time derivative of the signal DA+KWR (within the dotted rectangle 32) is adapted to perform the process of derivation electrically in such a manner that when it receives between its input terminals 30 and 3| a certain voltage it delivers across the leads 5'! and 58 a voltage varying substantially as the derivative with respect to time of the input voltage. The derivator consists of a capacitor 59 inserted between the terminal 38 and the lead 5?, and of the resistor 58 inserted between the terminal SI and the lead 57.

The operation of the derivator can be explained mathematically as follows: Let V1(T) be the function representing the voltage applied across the input terminals 33 and 3| of the derivator, V2(T) the function representing the voltage across the terminal 53 and the lead 57, C the capacitance of the capacitor 53, P the resistance of the resistor 59 and HT) the current flowing through the capacitor 59. Assume also that the leads 51. and 5B of the derivator have been disconnected from the tube BI and the battery 52. Consequently, the same current i(T) flows through the capacitance 59 and through the resistance BI] and the following relation holds true:

Differentiating the Equation 13, we obtain dV (l) l. di(T) dT -0 dT By selecting the proper values of the resistance P, for example making P negligibly small. the term d Consequently the expression Pi(T) which represents the voltage drop across the resistor 60 across the leads 5'! and 58 is substantially proportional to which represents the time derivative of the input voltage across the terminals 30 and 3|.

The voltage across the leads 51 and 53 is applied to the grid of a 3 electrode tube 6|, the cathode of which is connected to the terminal 58 by means of a biasing battery 52. A suitable B battery 53 and a resistor 54 are connected in the plate circuit. The two terminals of the resistor 64 are connected respectively to the terminals 33 and 34. It is well known that for a suitable choice of the type of the tube BI and batteries 62 and 63, the plate current is proportional to the grid voltage. As the plate current flows through the resistor 54 it is also proportional to the drop of voltage across this resistor, that is to say to the voltage across the terminals 33 and 34.

Consequently the voltage across the output terminals 33 and 34 represents the voltage across the leads 5? and 58 which is suitably amplified. As the voltage across the leads 51 and 58 is substantially proportional to the time derivative of the input voltage across the terminals 30 and 3|, then the output voltage across the terminals 33 and 34 represents r, i. e. the rate of progress of the drilling bit into the formation.

(5) The means for damping the fluctuations of the voltage across the terminals 33 and 34 (within the dotted rectangle without interfering with a sufliciently fast response of the instrument. The means comprises any kind of low-pass filter or simply a capacitor 68 shown on the Fig. 2.

(6) The means for producing a signal representing We comprised within the dotted rectangle |03 comprises the same parts as the means (3) comprised within the dotted rectangle H12 except the autotransformer 53, said autotransegeeaevi 9f? fcmner'being excluded from means I031 Other elements in means F03; such as thetransformer E IAE the rectifier SEA and the resistor 56A are identical to the correspondingelements 542 55 and '56 of the means 63). It is apparent that the output voltage of :the rectifier 55a, i. e. the voltage across the terminals 23A and 24A is representative of the weight Wa. Y

('7) The means for producing a signal representing' s comprised within the dotted: rectangle I I comprises as its essential element the tachometer generator I driven'by the rotary table Il through the bevel gears I 041 It is obvious that the output voltage" of the generator across the output terminals Hi6 and I01" represents the rotary angular velocity .9. I (8') The general arrangementotthe" computer is drawn diagrammatically on Fig. 3; Varibus elements of this arrangement are illustrated on Figures 4, 5B, 5C, 6; 83.80"; and 9 and various symbols on Figures 4A, 5A, 6A, 7A, 8A, and 9A. Figs.- 4- and' 4A show an integrating el'ement which comprises two input shafts I51, I6I and one output shaft I591 The angular displacement oft'he output shaft I 5'9 depends upon the angular displacementsof theinputshafts I 51, I 61 in accordance with a definite functional relationship which may be expressed as follows:

W'= Udv 17 V1 iii-which T0 designates the angular displacement of the shaft I 6I I V, designates the angular displacement of the shaft I5I,an 1 W designates the angular displacement of the shaft I59" The input motion V is impartedto' the shaft r51" which-rotates a flat disc I52 abouta vertical exist Asharp-edged wheel I53 rests on the disc and is driven by friction so as to produce the output rotation W of the shaft I59 when the disc is turned. The shaft I5! is driven by the wheel I53 through the spline shaft I54 and bevel gears: I58;v One' of the'bevel gears I 58 is slidinglymounted onthe' spline shaft I54. The motion: U displaces the spline shaf't'l54 along the direction of the axis of thesaid I shaft. During the displacement the bevel gears I 58 are continuously engaged one to another. The input motion U is applied to" the shaft I-6'I' which drives the threaded shaft I65 through the bevel gears I60. The shaft I55 moves the nut I5!- carrying-the output wheel I53. Let a designate the distance between the wheel I53 and the axis of the shaft I 5-I. It'is apparent that the ratio between the angular displacements of the shafts I54 and I5I is equal to the ratio of a and the radius of the wheel I53; on the other hand, the value a is evidently proportional to U. Consequently we have the following relation:

dW I v -J U (18) where his: a constant of the integrator. The Equation 18 gives e V W=bf UdV 19 By a suitable choice of units, dimensions, and ot-the ratio of gears I58, b can be made equal to one and-zthe integrator will operate according to the-Formula 17. Consequently if the shafts I6! and I'5l are driven so asto assume successive 1 16 angular positionsin'fiaccordance: with; the? sue cessive; values: of; functionsrU and V}. then-tile angular positionsiofs thersha'ft; law are equali to the values: of the; function 8751 defined witha the Formula 17';

The integrator is also used in the computento generate natural logarithms: If. the: shatter I59 and *I'BIF. are: connectedi so that; their displaces ments are. identical; then. the angular positions or the shaft: I'5Ii are: the. natural: logarithms' of the angular positions of: the shaits' #591 and: IZIiiIJ. Then, whenused to generatelnaturali logarithms; the: input shafts are? I59; and 1:6 I andtheiolllf put; shaft is: the; shaft? Ii5Ii.

The. mathematical explanati'oniis as follows; If-y::loge :c; then.

and dare-wily:

mfdrdr (20)" Comparing thisequation with the Equation. 117 itis seen that ifthe" functions Wand U: are identical, i. e. WzU, then V corresponds to y; i. e. v loge- U or V -loge W.

Consider now Figures 5A, 5B; and 5C illustrating a means for adding two: valuesand'; designated as adder. An adder is an instrument? prov-idled with two input shafts I62 and I63 and .one output shaft I64. The motion of. the shaft I6zkis equal to the sum of motions of the shafts I 62 and I63, i; e. that the shafts are interconnectedi'n such manner that at any moment the angular displacement'of theshaft I64 is equal to the sum of the angular displacements of the shafts I62 and I63; An adder is: essentially a differential off any type. A. planetary differentialwas drawn on Figures 513 and 5C. The-input shaft it: drives the gear 206 which drives the four planetary gears 20! placed. on the four small shafts208. The small shafts 2011- are fastenect on the: gear 2'63 driven by the input shaft I63 through thegear 2I0'. The four planetary gears 2.0-1 drive the gear 211 which drives the output shaft:- I'6l through the gear 212. The input shaft 162- andlthe gear 206 impart to the planetary gears 20 a motion which is a revolution about their axis. The Input shaft I63 and-the gears 2m and losimpart to the planetary gears 26'! a motion which is a. revolution of their axes about the axis of the shaft I62 Consequently; the four planetary gears 2M impart to the gearsZH and III and to the output shaft I 64 a motion which is a function of the two input motions. It may be clearly seen by those skilled in the art that by a properchoice of gears the motion ofthe output shaft I may be equal to the sum of the motions of the two input shafts I62 and I63.

In the computer described here, the adder is sometimes used as a subtractor. In suchcase the input shafts'are I64 and I62 and the output shaft is the shaft I 63." The motion of the shaft I63 is the difference of the motions of the shafts I64 andl62. V

Consider now Figures 6 and 6A illustrating a means for multiplying a variable value by a constant factor m and designated as multiplier. A multiplier comprises two gears 2 I3 and 2 I 4 and two shafts I65 and I66. The input shaft I 65 drives the gear 2I3 which drives the gear 214 which in turn drives the output shaft I66.

The ratio of number of teeth of the gears 2I3 and H4 is equal to the constant factor m of the multiplier.

Consider now Fig. 1A which shows diagrammatically a timing motor driving an output shaft 2I5 with a constant angular velocity. Any type of a commercially available synchronous motor, or a clock driven motor are suitable for the purpose.

Figures 8A, 8B, and 8C illustrate an electromagnetic transducer which is essentially an instrument transforming a D. C. voltage into angular positions of a shaft. The transducer is provided with a pair of electric input terminals I61 and IE8 and an output shaft I68. The angular positions of the output shaft I68 are proportional to the input voltage across the terminals I61 and I68. The transducer comprises essentially a solenoid attracting a bar magnet I1I which movement is opposed by a spring I12. The magnet is provided with a rack driving the pinion I13 so the rectilinear motion of the rack is transformed into a rotation of the pinion I13 which rotates the output shaft I88.

Figures 9 and 9A illustrate a very simple means used in the computer for driving a shaft 2I8 by another shaft 2 I5 perpendicular to the first. The means comprises two bevel gears 2 I1 and 2I8.

Consider now the general computer arrangement shown in Fig. 3. The arrangement is provided with three pairs of input terminals II6II1, II8II8, and II4II5 shown also in Fig. 2. These input terminals bring to the computer three signals that represent respectively:

(a) the value WR or weight suspended from the hook (b) the value 5 or rotary table angular velocity (c) the value r or rate of drilling The three electromagnetic transducers I14, I15, and I16 transform the input electric signals into mechanical motions of the shafts l11, I18, and I18.

The input shaft 220 must be set manually on an angular position corresponding to the total weight of the drilling string WT. The shafts 220 and I11 drive the shaft 2I8 through the adder 22I connected as a subtractor. As stated above the angular positions of the shaft I11 correspond to WR. Consequently the angular position of the shaft 2I9 is always equal to WT--WR which is equal to We according to the Formula 11.

The shaft I18 drives the shaft I80 through the multiplier IBI of ratio C. The motion of the shaft I80 is cs. 0 is a constant defined in connection with the Formula 2.

The shafts I18 and I80 drive the shaft I82 through an adder I83. Thus the motion of the shaft I82 is r-I-cs.

The shafts 2I8, I18, and I82 drive respectively the shafts I84, I85, and I86 respectively through the integrators I81, I88, and I88. The integrators are connected for generation of logarithms. Then the motions of the shafts I84, I85, and I88 are respectively log We, log s and log (r+cs).

The shafts I84 and I85 drive the shafts I80 and I8I respectively through the multipliers I82 and I93 of ratio equal to two. Thus the motions of the shafts I80 and I8I are respectively 2 log We and 2 log s.

The shafts I80 and I8I drive the shaft I84 through the adder I85. Thus the motion of the shaft I84 is: 2 log WB+2 log 3.

The shafts I84 and I88 drive the shaft I88 through the adder I81 working as a subtractor. Thus the motion of the shaft I86 is:

2 log WB+2 log s-log r+cs) The shaft I88 drives the shaft I88 through the 12 integrator I88 connected in such a manner that the input motion of the shaft I88 is the logarithm of the output motion of the shaft I88 which is then representative of It is desired to integrate the motion of the shaft I88 with respect to time. For this purpose a timing motor 20I drives the shaft 200. the motion of which is then a uniform one.

The shafts 200 and I88 drive the shaft 202 through an integrator 203. Thus the motion of the shaft 202 is i. e. the function B such as defined by the Equation 2. Referring to Fig. 2, the shaft 202 drives a hand 204 moving in front of a dial 205 on which the values of B are marked. Before starting drilling with a new bit the shaft 202 is turned to bring the hand 204 to zero position. Critical values of B for which different kinds and sizes of bits are dull are also marked on the dial 205.

The computer described above performs automatically all the calculations according to Formulas 2 and 11. As stated above the rate of drilling T used for such a computation must be a true rate of drilling, i. e. the rate of progress with which the bit enters the formation, and not the rate of progress of the downward motion of the upper part of the drilling string visible above the earth surface. Without departing from the scope of the appended claims, the computation might also be done not with Formula 2 which is an integral, i. e. a sum of infinitely small increments, but with a sum of finite increments. In such case different factors of the formula must be replaced as follows: dT per AT which is an increment such as 5 minutes for example.

We, s and 1 must be considered respectively as the average weight on bit, rotary angular velocity, and rate of drilling during the time interval AT. And the average rate of drilling is approximately the same when considering the rate of progress of the bit or the rate of progress of the upper portion of the drilling string. Consequently, the average rate of drilling is the progress of the downwards motion of the kelly during the time interval AT.

Various other alterations and changes may be made in the formula used for computation which general form is the relationship (1), in form and arrangement of the details of the described apparatus without departing from the scope of the appended claims.

What I claim and desire to secure by Letters Patent is:

1. Apparatus for indicating the degree of wear of a rotating bit attached to a rotary drilling string, comprising means for providing a signal representing the rate of downward progress of the bit, a weight responsive means for producing a signal representing a function of the weight applied to the bit, a computer for combining said signals to produce a resultant signal representing the quotient of said second signal over said first signal, said resultant signal representing the rate of wear of the bit and varying with time, said computer including an integrator for integrating said resultant ,si'mal. with itespectr to time.

.2. In. an arrangement for. rotary drilling itemploying a drilling string having a bitrattaehecl thereto and-comprisinga means cooperating with said drilling string for producing a signal representing the rate of downward progress of the bit, means responsive to said signal -for producing another signal that decreases with the increase of said first signal and an integrator .qperated -ini'a definite relationship to ,an independent variableprogressively increasing with time jfor integrating said other signal with respect, to said independentvariable to obtain ameasurement'of the degree of wear of the bit.

3. In an arrangement for rotary drilling employing a drilling string having a bit attached thereto and comprising a means cooperating with said drilling string for producing a signal the magnitude of which varies substantially in an inverse proportional relationship to the rate of downward progress of said bit, and a time driven mechanism responsive to said signal for integrating said varying magnitude with respect to time to obtain a measurement of the degree of wear of the bit.

4. In an arrangement for rotary drilling employing a drilling string having a bit attached thereto and comprising an independent means cooperating with said drilling string for producing a signal representing the rate of downward progress of said bit, another independent means for producing a signal representing a function of the weight applied to the bit, means responsive to said two signals for producing a resultant signal that increases with the decrease of said first signal and that increases with the increase of said second signal in accordance with a predetermined relationship and an integrator for integrating said resultant signal with respect to time to obtain a measurement of the degree of wear of the bit.

5. In an arrangement for rotary drilling employing a drilling string having a bit attached thereto and comprising a rate responsive means for producing a signal representing the rate of downward progress of said bit, a weight responsive means for producing a signal representing a function of the weight applied to the bit, a computer responsive to said two signals for producing a resultant signal that represents substantially a quotient obtained from dividing the magnitude representing a function of said weight over a magnitude representing said rate of progress, said computer comprising a time driven mechanism responsive to said resultant signal for integrating said resultant signal with respect to a variable that progressively increases with time to obtain a measurement of the degree of wear of the bit.

6. In an arrangement for rotary drilling employing a drilling string having a bit attached thereto and comprising a rate responsive means for producing a signal representing the rate R of the downward progress of said bit, a weight responsive means for producing a signal representing a function of the weight W applied to the bit, means for producing a signal representing the number of revolutions s of said bit per unit of time, a computer mechanism responsive to said three signals for producing a resultant signal representing the value Wa S b R d C S where a, b, c, and d are suitably chosen constants,

said computer includingian'iintegratormesponsive ito-rsaid resultant signal :ior .mtegratingtsaid. neissultant signal with respect .to :time. A

'7." Apparatus for indicating the degree of: mm of a rotating :bit attached *to .a .rotary drilling sstrin'g, comprising means for providinga :signal representing :the rate of the. downward iDIiOgllBSS of the-bit, a weight responsive :means ion pro-- ducing :a signal erepresentingia function-rat ,the weight applied 'to athebit, means z-responsivegtp 'saidzsignalls for producing a resultant =-sig-nalcnep.- =r.esenting.:the irate :oiwear :of tthexbit, .said fresultant signal varying. with ;respect ato aan finds,- tpendentwariable that progressivelyincneases time, and an integrator for integrating said resultant signal with respect to said variable.

8. In an arrangement for rotary drilling employing a drilling string having a bit attached thereto and comprising a rate responsive means for producing a signal representing the rate of the downward progress of said bit, a weight responsive means for producing a signal representing a function of the weight applied to the bit; means for producing a signal representing the angular velocity of said bit, means responsive to said three signals for producing a resultant signal representing the rate of wear of said bit, and an integrator for integrating said resultant signal with respect to time.

9. Apparatus for indicating the degree of wear of a rotating bit attached to a rotary drilling string, comprising means for providing a signal representing the rate of the downward progress of the bit, a weight responsive means for producing a signal representing a function of the weight applied to the bit, means for producing a signal representing the angular velocity of the bit, means responsive to said signals for producing a resultant signal representing the rate of wear of the bit, said resultant signal increasing with the increase of said second signal and decreasing with the increase of said first signal, and an integrator for integrating said resultant signal with respect to time.

10. Apparatus for indicating the degree of wear of a rotating bit attached to a rotary drilling string comprising means for providing a signal representing the downward progress of the bit, a weight responsive means for producing a signal representing a function of the weight applied to the bit, means for producing a signal representing the angular velocity of the bit, means for combining said second and third signals into a resultant signal, means responsive to said resultant signal and said first signal for producing a signal representing the quotient of said resultant signal over said first signal, said quotient representing the rate of wear of said bit, and an integrator for integrating said quotient representing signal with respect to time.

11. Apparatus for indicating the degree of wear of a rotating bit attached to a rotary drilling string comprising means for providing a signal representing the rate of downward progress of the bit, a weight responsive means for producing a signal representing a function of the weight applied to the bit, means for producing a signal representing the angular velocity of the bit, means for combining said first and third signals into a resultant signal, means responsive to said second signal and said resultant signal for producing a signal representing the quotient of said second signal over said resultant signal, said 7 quotient representing the rate of wear of said bit and an integrator for integrating said quotient representing signal with respect to time.

12. Apparatus for indicating the degree of wear or a rotating bit attached to a rotary drilling string, comprising means for providing a. signal representing the rate of the downward progress of the bit, a weight responsive means for producing a signal representing a function of the weight applied to the bit, means for producing a signal representing the angular velocity of the bit, means for combining the first and third signals into a resultant signal, means for combining the second and third signals into a resultant signal, means responsive to said two resultant signals for producing a signal representing a quotient of said second resultant signal 16 over said first resultant signal, said quotient representing the rate of wear of said bit, and an integrator for integrating said quotient representing signal with respect to time.

ARTHUR LUBINSKI.

References Cited in the file of this patent UNITED STATES PATENTS Number Name Date 10 2,298,222 McShane Oct. 6, 1942 I 2,330,753 Sikes, Jr Sept. 28, 1943 2,365,014 Silverman et a1. Dec. 12 ,1944 2,422,806 Silverman et a1. June 24, 1947 

